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# GATE | GATE-CS-2015 (Set 3) | Question 54

• Last Updated : 19 Nov, 2018

Given the function F = Pâ€² + QR, where F is a function in three Boolean variables P, Q and R and Pâ€² = !P, consider the following statements.

```  S1: F = Î£ (4, 5, 6)
S2: F = Î£ (0, 1, 2, 3, 7)
S3: F = Î  (4, 5, 6)
S4: F = Î  (0, 1, 2, 3, 7) ```

Which of the following is true?
(A) S1-False, S2-True, S3-True, S4-False
(B) S1-True, S2-False, S3-False, S4-True
(C) S1-False, S2-False, S3-True, S4-True
(D) S1-True, S2-True, S3-False, S4-False

Explanation: After drawing K map of F = P` + QR ,we can find out S2 and S3 are TRUE.

Alternate Explanation :

```P Q R = (!P + QR)

0 => 0 0 0 => 1+0.0 =1 =>Î£

1 => 0 0 1 => 1+0.1 =1 =>Î£

2 => 0 1 0 => 1+1.0 =1 =>Î£

3 => 0 1 1 => 1+1.1 =1 =>Î£

4 => 1 0 0 => 0+0.0=0 =>Î

5 => 1 0 1 => 0+0.1=0 =>Î

6 => 1 1 0 => 0+1.0=0 =>Î

7 => 1 1 1 => 0+1.1=1 =>Î£

as sigma means 1 and pi means 0
therefore Î£ = (0,1,2,3,7)
Î  = (4,5,6)
```
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